Q.Derive ionic radius using Pauling's method.

Pauling's method finds individual ionic radii by assuming radius is inversely proportional to effective nuclear charge, and splitting the known inter-ionic (cation-anion) distance in that inverse ratio.

For a set of isoelectronic ions (ions having the identical number of electrons and hence the same electronic configuration, differing only in nuclear charge — e.g. Na+, Mg2+, Al3+, all having the Ne configuration with 10 electrons), Pauling assumed that the radius of each ion is inversely proportional to its effective nuclear charge, Zeff, experienced by the outermost electron shell:

r proportional to (1 / Zeff), i.e., r = C / Zeff

where Zeff = Z - s (Z is the actual nuclear charge/atomic number, and s is a screening constant that accounts for the shielding of outer electrons by inner-shell electrons; Pauling used standard screening-constant values worked out for each type of noble-gas-like configuration), and C is a proportionality constant appropriate to that isoelectronic series (depending on the principal quantum number of the outer shell).

To obtain actual numerical radii, Pauling combined this relation with experimentally measured inter-ionic distances (from X-ray crystallography) in an ionic crystal. For a crystal made of a cation and an anion, the observed cation-anion distance d equals the sum of their individual radii:

d = r(cation) + r(anion)

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